Question: Suppose that A, B, and D are any three events such that Pr(A|D) Pr(B|D) and Pr(A | Dc) Pr(B | Dc). Prove that

Suppose that A, B, and D are any three events such that Pr(A|D) ≥ Pr(B|D) and Pr(A | Dc) ≥ Pr(B | Dc). Prove that Pr(A) ≥ Pr(B).

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